Related papers: Determining eigenstates and thermal states on a qu…
We propose a hybrid quantum-classical algorithm for solving QUBO problems using an Imaginary Time Evolution-Mimicking Circuit (ITEMC). The circuit parameters are optimized to closely mimic imaginary time evolution, using only single- and…
Approximate combinatorial optimization is a promising use case for quantum computers. The quantum optimization algorithms often employ a fixed ansatz that evolves an unbiased initial state towards states with better values of the optimand,…
Hamiltonian diagonalization is at the heart of understanding physical properties and practical applications of quantum systems. It is highly desired to design quantum algorithms that can speedup Hamiltonian diagonalization, especially those…
In the pursuit of numerically identifying the ground state of quantum many-body systems, approximate quantum wavefunction ansatzes are commonly employed. This study focuses on the spectral decomposition of these approximate quantum…
We present an algorithm that uses block encoding on a quantum computer to exactly construct a Krylov space, which can be used as the basis for the Lanczos method to estimate extremal eigenvalues of Hamiltonians. While the classical Lanczos…
Quantum algorithms for simulating electronic ground states are slower than popular classical mean-field algorithms such as Hartree-Fock and density functional theory, but offer higher accuracy. Accordingly, quantum computers have been…
The preparation and computation of many properties of quantum Gibbs states is essential for algorithms such as quantum semidefinite programming and quantum Boltzmann machines. We propose a quantum algorithm that can predict $M$ linear…
The computation of thermal properties of quantum many-body systems is a central challenge in our understanding of quantum mechanics. We introduce the Quantum Finite Temperature Lanczos Method (QFTLM), which extends the finite-temperature…
The computational complexity of simulating quantum many-body systems generally scales exponentially with the number of particles. This enormous computational cost prohibits first principles simulations of many important problems throughout…
We use matrix product techniques to investigate the performance of two algorithms for obtaining the ground state of a quantum many-body Hamiltonian $H = H_A + H_B$ in infinite systems. The first algorithm is a generalization of the quantum…
The efficient simulation of quantum dynamics and ground states is a central challenge in physics and a key frontier for quantum advantage. While short-time evolution in one-dimensional systems can often be simulated classically, extending…
In this thesis, I investigate aspects of local Hamiltonians in quantum computing. First, I focus on the Adiabatic Quantum Computing model, based on evolution with a time dependent Hamiltonian. I show that to succeed using AQC, the…
Models of interacting many-body quantum systems that may realize new exotic phases of matter, notably quantum spin liquids, are challenging to study using even state-of-the-art classical methods such as tensor network simulations. Quantum…
Solving finite-temperature properties of quantum many-body systems is generally challenging to classical computers due to their high computational complexities. In this article, we present experiments to demonstrate a hybrid…
We revisit quantum phase estimation algorithms for the purpose of obtaining the energy levels of many-body Hamiltonians and pay particular attention to the statistical analysis of their outputs. We introduce the mean phase direction of the…
The variational principle of quantum mechanics is the backbone of hybrid quantum computing for a range of applications. However, as the problem size grows, quantum logic errors and the effect of barren plateaus overwhelm the quality of the…
We identify quantum imaginary time evolution as a Riemannian gradient flow on the unitary group. We develop an upper bound for the error between the two evolutions that can be controlled through the step size of the Riemannian gradient…
The problem of simulating the thermal behavior of quantum systems remains a central open challenge in quantum computing. Unlike well-established quantum algorithms for unitary dynamics, \emph{provably efficient} algorithms for preparing…
It is of great interest to understand the thermalization of open quantum many-body systems, and how quantum computers are able to efficiently simulate that process. A recently introduced disispative evolution, inspired by existing models of…
The quantum imaginary time evolution (QITE) methodology was developed to overcome a critical issue as regards non-unitarity in the implementation of imaginary time evolution on a quantum computer. QITE has since been used to approximate…